I will defend a principle at work in Thomas Aquinas’s argument that the human intellect must be immaterial in order to know material things in SummaTheologica, Ia, q.75, a.2. Thomas relies on the position that whatever knows certain things would be impeded in this knowledge if it contained in itself thesesame things. Thus, if humans can, in principle, know all material things, then the intellect cannot be material. The position that a material intellect would be limited in knowledge of material things is perhaps the most controversial part of the argument. I will articulate a version of this argument and argue that two objections to Thomas’s argument, offered by Norman Kretzmann and Robert Pasnau, fail, due in large part to a misunderstanding of proper objects of cognition